Solve 7m^2=21m

$$7 m ^ { 2 } = 21 m$$

Solve for m

$$m=3$$

$$m=0$$

Steps Using Factoring

Subtract 21m from both sides.

$$7m^{2}-21m=0$$

Factor out m.

$$m\left(7m-21\right)=0$$

To find equation solutions, solve m=0 and 7m-21=0.

$$m=0 m=3$$

Steps Using the Quadratic Formula

Subtract 21m from both sides.

$$7m^{2}-21m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -21 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2\times 7}$$

Take the square root of \left(-21\right)^{2}.

$$m=\frac{-\left(-21\right)±21}{2\times 7}$$

The opposite of -21 is 21.

$$m=\frac{21±21}{2\times 7}$$

Multiply 2 times 7.

$$m=\frac{21±21}{14}$$

Now solve the equation m=\frac{21±21}{14} when ± is plus. Add 21 to 21.

$$m=\frac{42}{14}$$

Divide 42 by 14.

$$m=3$$

Now solve the equation m=\frac{21±21}{14} when ± is minus. Subtract 21 from 21.

$$m=\frac{0}{14}$$

Divide 0 by 14.

$$m=0$$

The equation is now solved.

$$m=3 m=0$$

Steps for Completing the Square

Subtract 21m from both sides.

$$7m^{2}-21m=0$$

Divide both sides by 7.

$$\frac{7m^{2}-21m}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$m^{2}+\left(-\frac{21}{7}\right)m=\frac{0}{7}$$

Divide -21 by 7.

$$m^{2}-3m=\frac{0}{7}$$

Divide 0 by 7.

$$m^{2}-3m=0$$

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-3m+\left(-\frac{3}{2}\right)^{2}=\left(-\frac{3}{2}\right)^{2}$$

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-3m+\frac{9}{4}=\frac{9}{4}$$

Factor m^{2}-3m+\frac{9}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$m-\frac{3}{2}=\frac{3}{2} m-\frac{3}{2}=-\frac{3}{2}$$

Add \frac{3}{2} to both sides of the equation.

$$m=3 m=0$$